HONG KONG—In November, on the 24th floor of a Hong Kong hotel, eight investors representing trillions of dollars convened to hear details from major iPhone assembler Hon Hai Precision Industry Co. about its long-term business strategy. What they got was just a single document that some in the room had already seen months earlier.

The odd moment was the latest exchange between Hon Hai and some of its big foreign shareholders, who are calling for the world’s largest contract electronics manufacturer by revenue to raise its dividend...